Numerical solving for dynamic response of fractional order damped structure based on linear time-invariant system equivalence
GUO Qin1,2, CHEN Taicong1,2
1.State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China;
2.Pazhou Lab, Guangzhou 510335, China
Abstract:Fractional derivative is a comon expression of the constitutive model of a damper. The analytical solution of the dynamic response of the relevant structure is difficult to obtain, and an efficient time-domain numerical solution is of practical importance. In this paper, for the widely used Riemann-Liouville type fractionally damped structure, the Adams-Moulton algorithm based on multi-step predictor-corrector mechanism is introduced to calculate the fractional derivatives, and then the equivalent linear and time-invariant dynamical system is constructed at each discrete time instant, and finally the Newmark-β numerical integration scheme is combined to establish the explicit computation formula at each time instant to achieve direct and rapid solution of high-accuracy dynamic responses. Taking a SDOF oscillator subjected to harmonic loading and unit impulse as an example, the analytical solution, two direct numerical solutions, and the present method are compared to verify the high accuracy and stability of the present method. Finally, for the example of a multi-layer damped structure subjected to seismic excitation, the iterative numerical algorithm, the engineering approximation algorithm, and the present method are compared and investigated to further verify the combined advantages of the present method in terms of computational accuracy and computational efficiency, and to reveal the potential of engineering applications.
郭琴1,2,陈太聪1,2. 基于线性定常系统等效的分数阶阻尼结构动力响应数值求解[J]. 振动与冲击, 2023, 42(15): 138-143.
GUO Qin1,2, CHEN Taicong1,2. Numerical solving for dynamic response of fractional order damped structure based on linear time-invariant system equivalence. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(15): 138-143.
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